Problem: The following line passes through point $(2, -2)$ : $y = -\dfrac{6}{7} x + b$ What is the value of the $y$ -intercept $b$ ?
Substituting $(2, -2)$ into the equation gives: $-2 = -\dfrac{6}{7} \cdot 2 + b$ $-2 = -\dfrac{12}{7} + b$ $b = -2 + \dfrac{12}{7}$ $b = -\dfrac{2}{7}$ Plugging in $-\dfrac{2}{7}$ for $b$, we get $y = -\dfrac{6}{7} x - \dfrac{2}{7}$. ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ $(2, -2)$